Number theory help. How did they conclude gh = 1? (at the bottom of page 17)

Question

anonymous · Answer

https://books.google.com/books?id=eVwvvwZeBf4C&lpg=PA3&pg=PA17#v=onepage&q&f=false

usukidoll · Answer

Oh I love that book. I've used it last year.

freckles · Answer

how far did you get because right before they say that they have d=ghd 
and dividing d on both sides gives 1=gh (Assuming d isn't 0 )

anonymous · Answer

@UsukiDoll yeah I like it too. Certainly better than the one wrote by Stein

freckles · Answer

also we know d isn't zero since it is given in the theorem that a and b are not 0

anonymous · Answer

O: oh, I see it now.

anonymous · Answer

The whole time i was reading d2 = gh d1 .

anonymous · Answer

This question is a false alarm XD. I was having a brain fart :P sorry people lol

usukidoll · Answer

d = ghd ... when d was divided it left 
1 = gh 

so g = 1 and h = 1 
which are the only values that satisfy 
1=gh

usukidoll · Answer

xD I'm still wondering how people master proofs x.x like I don't mind easy ones, but the hard ones are crazy

anonymous · Answer

@freckles thanks for clarifying :)

anonymous · Answer

You know what. While we're at it, can any one explain how they got 0 <= r_i <= b-i?

mathstudent55 · Answer

$gd_1 = d_2$  and   $hd_2 = d_1$

                         $d_2 = \dfrac{d_1}{h} $

Equate the two expressions for $d_2$

$gd_1 = \dfrac{d_1}{h} $

$ghd_1 = d_1$

$gh = 1$

anonymous · Answer

They said it's by induction though :/

@mathstudent55 thank you. I got that part :)